CN115544690B - Numerical reconstruction and heat transfer characteristic evaluation method for microcrack-containing thermal barrier coating microstructure - Google Patents
Numerical reconstruction and heat transfer characteristic evaluation method for microcrack-containing thermal barrier coating microstructure Download PDFInfo
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Abstract
The invention discloses a numerical reconstruction and heat transfer characteristic evaluation method of a micro-crack-containing thermal barrier coating microstructure, which comprises the steps of determining a simulation area and size setting, generating random micro-cracks with different morphological characteristics, placing the micro-cracks in the simulation area to judge whether the space occupied by the micro-cracks reaches the porosity ratio of preset micro-cracks, establishing a general pore model of the thermal barrier coating based on a four-parameter growth method, reconstructing the real mesoscopic morphology of TBCs, judging whether the thermal barrier coating reaches the preset volume fraction or not, and establishing a heat transfer analysis model based on a thermal lattice Boltzmann method to calculate heat insulation performance parameters such as temperature distribution, heat conductivity and the like. Compared with the prior art, the model can more truly and effectively restore the mesostructure of the coating, thereby reducing the cost consumption caused by scanning a large amount of real coating samples and more accurately predicting the heat insulation effect of TBCs.
Description
Technical Field
The invention relates to the technical field of porous media, in particular to a method for reconstructing numerical values and evaluating heat transfer characteristics of a microcrack-containing thermal barrier coating microstructure.
Background
In order to meet the long life and high reliability requirements of turbine blades, it is desirable to coat the surface of high performance aircraft engine turbine blades with a thermal barrier coating. The thermal barrier coating technology has wide application prospect in the fields of aerospace, weapons, ships and the like. TBCs made of ceramic materials have the characteristics of high temperature resistance, corrosion resistance, high strength, low heat conduction and the like, and the service life and the running reliability of an engine are directly influenced by the heat insulation effect. TBCs systems generally include a ceramic layer, a bonding layer, and a superalloy substrate three-layer structure. Wherein, the bonding layer mainly adopts MCrAlY alloy (M refers to Fe, ni, co and the like), and because the bonding layer is subjected to thermal cycle oxidation for a long time in the service process, when the Al content is consumed to the extent that the Al2O3 growth cannot be satisfied, a thermally grown oxide is formed on the interface of the ceramic layer and the transition layer, thereby becoming the center of microcrack initiation. Stress concentration can be generated by initiation and further expansion of microcracks, so that the temperature distribution condition of the coating is greatly changed, and the heat insulation performance, the service efficiency and the durability of the coating are affected.
Because microcracks in TBCs do not have obvious regularity, some students mainly establish an ideal model to analyze the influence of microcracks on the temperature distribution characteristics and the heat insulation performance of the thermal barrier coating by simplifying the microstructure of the coating. However, the research is aimed at presetting microcracks of single composition, and directly simplifying the microcracks into spherical, ellipsoidal or flaky shapes with the same length, the same direction or the same size. In the actual case, the TBCs contain microcracks with random distributions of different sizes, inclinations, numbers, positions and morphologies. The oversimplified hypothesis model has larger deviation from the actual situation, and the calculation result has no universality and applicability.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for reconstructing the numerical value and evaluating the heat transfer characteristic of a micro-crack-containing thermal barrier coating microstructure so as to solve the technical problem about larger deviation between a simplified model of the micro-crack-containing thermal barrier coating pore structure and a real coating structure.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a method for numerical reconstruction and heat transfer characteristic evaluation of a microcrack-containing thermal barrier coating microstructure, the method comprising:
s1, determining simulation areas and size settings, including settings of a physical model and a simulation calculation grid; based on a Monte Carlo simulation method and a four-parameter growth method, generating random microcracks with different morphological characteristics;
s2, changing the inclination directions of different microcracks according to a certain statistical rule through a coordinate transformation method, then placing the microcracks in a simulation area, and judging whether the space occupied by the microcracks reaches the porosity ratio of the preset microcracks or not;
s3, establishing a general pore model of the thermal barrier coating based on a four-parameter growth method, wherein a solid framework in the thermal barrier coating is used as a growth phase, pores are non-growth phases, the setting of the porosity controls the pore volume fraction of the coating, and the generation probability of a nucleation center of the solid framework is set to control the number of the pores; traversing the initial randomly distributed growth nuclear nodes, randomly growing each growth nuclear node in a three-dimensional space, controlling the generation of thermal barrier coatings of different structures according to growth nuclear probability of 26 directions under three-dimensional coordinates, wherein the growth nuclear probability of the layered structure coating in the horizontal direction is far greater than that in the vertical direction, and the columnar structure coatings are opposite;
s4, overlapping the general pore structure into a simulation area containing microcracks to generate a coating pore model coupling the microcrack defects, reconstructing the real mesoscopic morphology of TBCs, and judging whether the preset volume fraction is reached;
s5, establishing a heat transfer analysis model based on a thermal lattice Boltzmann method to calculate heat insulation performance parameters such as temperature distribution, heat conductivity and the like.
In the step S1, the micro-crack morphology under a certain statistical distribution rule is generated by using a monte carlo algorithm:
s1.1 generates random numbers uniformly distributed over the [0,1] interval:
the iterative formula of the linear congruence method for generating the random number is as follows:
x n ＝(ax n-1 +c)(modM)
wherein: a is a non-negative multiplier; c is a non-negative increment; m is a modulus, (mod M) represents the remainder divided by M.
And then obtaining random numbers R uniformly distributed on the intervals of [0,1 ]:
s1.2, generating random numbers of other specified statistical distribution rules by using uniform random number calculation:
random numbers obeying other distribution types can be generated by using the uniform random numbers on the [0,1] interval generated in the step (1);
the probability density function as a uniform distribution is:
the method for calculating the random variable comprises the following steps:
x f ＝(b-a)R+a
wherein: x is x f Is the random number that is calculated; r is interval [0,1]]Random numbers uniformly distributed on the base;
s1.3, changing the orientation of microcracks by coordinate translation and rotation transformation:
there are a base coordinate system 0 and a moving coordinate system I, the postures of the base coordinate system 0 and the moving coordinate system I are the same, and the origins are not coincident. The coordinates of any particle P in the space and fixedly connected with the coordinate system I in the coordinate system 0 are expressed as P 0 ＝[p 0x p 0y p 0z ] T The coordinates in the coordinate system I are denoted as P 1 ＝[p 1x p 1y p 1z ] T Origin O of coordinate system I 1 In the coordinate system 0, the coordinates are
There is ∈according to vector operation rules>
If the attitude change matrix of the coordinate system I relative to the coordinate system 0 is considered, the relative relationship between the two can be considered as the combination of translational motion between the origins and pure rotation around the origins, and the following are: />
Is of the same kind
Where Rot represents the basic rotation, written in a matrix in three-dimensional coordinates in the form of:
the above marks are rotated by alpha, phi and theta angles around x, y and z axes respectively;
s1.4, generating microcracks, and controlling the growth probability in the length/width direction to be 100/1 by using a QGS method to ensure that the microcracks are wedge-shaped; controlling the thickness direction of a single micro-crack to only have two layers of grids, so as to ensure that the micro-crack is approximately of a lamellar structure; then randomly generating a nucleation center point (x) according to a certain statistical distribution rule by using a Monte Carlo method 0 ,y 0 ,z 0 ) Morphology parameters such as inclination phi, inclination angle theta, length, quantity and the like. Nucleation center point (x) 0 ,y 0 ,z 0 ) As the growth core center of QGS microcracks, the lengths of the microcracks control the growth probabilities of the microcracks in different directions, and the trend phi and the dip angle theta are used as the basis of coordinate rotation transformation, so that microcracks with different shapes, sizes, directions and the like distributed according to a certain statistical rule are generated.
In the step S4, the initial growing nuclear node and the growing nuclear node after the growing are circularly traversed, which does not involve the continuous growing of the individual nodes; and the growth phase avoids the growth of micro-cracks in the simulation area and does not coincide with the micro-cracks, and the sum of the porosities of the micro-cracks and the common porosity is equal to the preset total porosity. 26 directions are included in the three-dimensional coordinate, the three-dimensional coordinate comprises 6 main directions, 12 face angle directions and 8 individual diagonal directions, a growing nuclear node is taken as a growing origin, a skeleton regenerates random numbers to non-pore adjacent points in the 6 main directions, and when the generated random numbers are smaller than the growing nuclear growth probability, the point grows to be a growing nuclear node; this step is repeated until the growth phase meets a preset volume fraction.
It should be noted that, the control equation of the heat conduction in the step S5 may be described as:
wherein the subscript f represents air in the pores, s represents a solid skeleton, T represents the temperature of the material, ρ, λ and c p Respectively representing density, heat conductivity coefficient and constant pressure specific heat capacity;
based on the above, a D3Q19 thermal lattice Boltzmann model is adopted, and a temperature evolution equation is as follows:
where r is a position vector, t is time, delta t Is a time step, α=0, 1, …,18 representing 19 discrete speed directions, where e α Is a discrete speed distributed type:
g eq (r, t) represents an equilibrium distribution function of temperature, as shown in the following formula:
the relationship between dimensionless relaxation time τ and thermal diffusivity λ is:
both the grid interface and the gas-solid boundary conditions adopt an unbalanced extrapolation format:
g α (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )-g α (ne) (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )+[g α (r,t)-g α eq (r,t)]
the corresponding macroscopic temperature and heat flux density can be determined by:
after the temperature field is determined, the effective heat conductivity lambda can be obtained eff The calculation formula of (2) is as follows:
λ eff ＝qδ/ΔT
where q is the steady state heat flow through the coating with a thickness δt, Δt representing the upper and lower boundary temperature difference.
In addition, the calculation method selects the same value (ρc p ) The value of (ρc) as air can be used in the actual simulation p ) The value is taken as a reference value; for the common solid and air in the pores, in order to reflect the difference of the heat conducting property of the two, it is ensured that (tau gf -0.5)/(τ gs -0.5)＝λ f /λ s And τ e (0.5-2.0) is generally set in lattice units to ensure convergence of the simulation.
The model has the beneficial effects that the model can more truly and effectively restore the mesostructure of the coating, thereby reducing the cost consumption caused by scanning a large amount of real coating samples and more accurately predicting the heat insulation effect of TBCs.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 shows the probability of growth of individual microcracks in different directions according to the invention;
FIG. 3 is a schematic view of the morphology of the individual wedge-shaped lamellar microcracks of the present invention at different angles, wherein FIG. 3 (a) is an x-z cross-section, FIG. 3 (b) is a y-z cross-section, FIG. 3 (c) is an x-y cross-section, and FIG. 3 (d) is a three-dimensional front view;
FIG. 4 is a schematic diagram of a model of a plurality of microcracks according to the present invention, wherein FIG. 4 (a-d) shows the morphology of microcracks with different statistical distribution laws;
FIG. 5 is a schematic view of the general pore model of the thermal barrier coating of the present invention, wherein FIG. 5 (a) is a layered structure coating, FIG. 5 (b) is a porous structure coating, and FIG. 5 (c) is a columnar structure coating;
FIG. 6 is a schematic view in y-z cross-section of a layered structure coating containing microcracks according to the present invention;
FIG. 7 is a schematic representation of simulated coating temperature field distribution according to the present invention, wherein FIG. 7 (a) shows a layered structure coating temperature field containing (a 1) no or (a 2-5) different sized microcracks and FIG. 7 (b) shows a columnar structure coating temperature field containing (b 1) no or (b 2-5) different sized microcracks at the same crack/pore ratio.
FIG. 8 is a graph of a numerical simulation versus literature comparison of effective thermal conductivity of a coating of the present invention as a function of microcrack parameters.
Detailed Description
The following description of the present invention will further illustrate the present invention, and the following examples are provided on the premise of the present technical solution, and the detailed implementation and the specific operation procedure are given, but the protection scope of the present invention is not limited to the present examples.
Examples
As shown in FIG. 1, the invention relates to a method for evaluating the numerical reconstruction and heat transfer characteristics of a microcrack-containing thermal barrier coating microstructure, which has lower use cost and can truly and effectively characterize the internal structural morphology of the coating, and specifically comprises the following steps:
step S1: determining simulation areas and size settings, mainly comprising the settings of a physical model and a simulation calculation grid; random microcracks with different morphological characteristics (the characteristic parameters comprise the number of the cracks, the length, the inclination angle, the position coordinates of a central point and the like) are generated based on a Monte Carlo simulation method and a four-parameter growth method.
Generating a microcrack morphology (comprising the number of cracks, the length, the inclination angle, the central point position coordinates and the like) under a certain statistical distribution rule by utilizing a Monte Carlo algorithm:
(1) Generating uniformly distributed random numbers over the [0,1] interval:
the iterative formula of the linear congruence method for generating the random number is as follows:
x n ＝(ax n-1 +c)(modM)
wherein: a is a non-negative multiplier; c is a non-negative increment; m is a modulus, (mod M) represents the remainder divided by M.
And then obtaining random numbers R uniformly distributed on the intervals of [0,1 ]:
(2) Generating random numbers of other specified statistical distribution rules by using uniform random number calculation:
with the uniform random numbers over the [0,1] interval generated in (1), random numbers following other distribution types (e.g., uniform distribution, exponential distribution, normal distribution, lognormal distribution, etc.) can be generated.
The probability density function as a uniform distribution is:
the method for calculating the random variable comprises the following steps:
x f ＝(b-a)R+a
wherein: x is x f Is the random number that is calculated; r is interval [0,1]]Random numbers uniformly distributed on the base.
(3) The coordinate translation and rotation transformation effects a change in the orientation of the microcracks:
there are a base coordinate system 0 and a moving coordinate system I, the postures of the base coordinate system 0 and the moving coordinate system I are the same, and the origins are not coincident. The coordinates of any particle P in the space and fixedly connected with the coordinate system I in the coordinate system 0 are expressed as P 0 ＝[p 0x p 0y p 0z ] T The coordinates in the coordinate system I are denoted p1= [ P 1x p 1y p 1z ] T Origin O of coordinate system I 1 In the coordinate system 0, the coordinates are
There is ∈according to vector operation rules>
If the attitude change matrix of the coordinate system I relative to the coordinate system 0 is considered, the relative relationship between the two can be considered as the combination of translational motion between the origins and pure rotation around the origins, and the following are: />
Is of the same kind
Where Rot represents the basic rotation, written in a matrix in three-dimensional coordinates in the form of:
the above equation identifies rotation by an angle α, φ, θ about the x, y, z axes, respectively.
(4) Microcrack generation
Generating single microcracks and determining the morphology of the single microcracks by using a QGS method:
the micro-cracks are generally in a wedge-shaped lamellar shape, and the micro-cracks can be ensured to be in a wedge shape by controlling the growth probability in the length/width direction to be 100/1 by using a QGS method as shown in fig. 2, and the structure of the wedge-shaped micro-cracks is shown in fig. 3 (c); controlling the thickness direction of single microcracks to be 2 μm only by two layers of grids, so as to ensure that the microcracks are approximately lamellar structures, as shown in fig. 3 (a) and 3 (b); fig. 3 (d) is a three-dimensional front view of a single wedge-layer lamellar microcrack that is generated.
Then randomly generating the nucleation in accordance with a certain statistical distribution rule by using a Monte Carlo methodHeart point (x) 0 ,y 0 ,z 0 ) Morphology parameters such as inclination phi, inclination angle theta, length, quantity and the like. Nucleation center point (x) 0 ,y 0 ,z 0 ) As the growth core center of QGS microcracks, the lengths of the microcracks control the growth probabilities of the microcracks in different directions, and the trend phi and the dip angle theta are used as the basis of coordinate rotation transformation, so that microcracks with different shapes, sizes, directions and the like distributed according to a certain statistical rule are generated.
Step S2: and further, different microcracks are placed in a simulation area after the inclination directions of the microcracks are changed according to a certain statistical rule by a coordinate transformation method, fig. 4 is a schematic diagram of a model of a plurality of microcracks in the invention, and fig. 4 (a-d) shows the appearance of the microcracks under different statistical distribution rules. And judging whether the space occupied by the microcracks reaches the porosity ratio of the preset microcracks or not.
Step S3: establishing a general pore model of the thermal barrier coating based on a four-parameter growth method, wherein a solid framework in the thermal barrier coating is used as a growth phase, pores are non-growth phases, the setting of the porosity controls the pore volume fraction of the coating, and the setting of the generation probability of a nucleation center of the solid framework controls the number of the pores; traversing the initial randomly distributed growth nucleus nodes, randomly growing each growth nucleus node in a three-dimensional space, controlling the generation of thermal barrier coatings with different structures (porous, lamellar and columnar structures) according to growth nucleus growth probabilities of 26 directions under three-dimensional coordinates, wherein the growth nucleus growth probability of the lamellar structure coating in the horizontal direction is far greater than that of the columnar structure coating, the columnar structure coating is opposite, and FIG. 5 is a schematic structural diagram of a general pore model of the thermal barrier coating. Fig. 5 (a) shows a layered structure coating, fig. 5 (b) shows a porous structure coating, and fig. 5 (c) shows a columnar structure coating.
Step S4: and superposing the general pore structure into a simulated region containing microcracks to generate a coating pore model coupling the microcrack defects, reconstructing the real mesomorphology of TBCs, and judging whether the preset volume fraction is reached. FIG. 6 is a schematic view of a y-z axis cross section of a layered structured coating containing microcracks according to the present invention, showing the apparent layered structure of the coating cross section, with a large number of unbonded areas between the layers, and a large number of microcracks and spherical micropores within the layers, which is highly similar to the true morphology of a thermal barrier coating. The algorithm is to circularly traverse the initial growth nuclear node and the growth nuclear node after growth, and does not relate to the condition of continuous growth of single nodes; and the growth phase avoids the growth of micro-cracks in the simulation area and does not coincide with the micro-cracks, and the sum of the porosities of the micro-cracks and the common porosity is equal to the preset total porosity. The three-dimensional coordinate has 26 directions in total, including 6 main directions, 12 facing angle directions and 8 opposite angle directions, the growing nuclear node is taken as the growing origin, the skeleton regenerates random numbers to the non-pore adjacent points in the 6 main directions, and when the generated random numbers are smaller than the growing nuclear growth probability, the point grows to be the growing nuclear node. This step is repeated until the growth phase meets a preset volume fraction.
Step S5: and establishing a heat transfer analysis model based on a thermal lattice Boltzmann method to calculate heat insulation performance parameters such as temperature distribution, heat conductivity and the like. Compared with the prior art, the model can more truly and effectively restore the mesostructure of the coating, thereby reducing the cost consumption caused by scanning a large amount of real coating samples and more accurately predicting the heat insulation effect of TBCs.
The control equation for heat conduction can be described as:
wherein the subscript f represents air in the pores, s represents a solid skeleton, T represents the temperature of the material, ρ, λ and c p Respectively representing density, heat conductivity coefficient and constant pressure specific heat capacity.
Based on the above, a D3Q19 thermal lattice Boltzmann model is adopted, and a temperature evolution equation is as follows:
where r is a position vector, t is time, delta t Is a time step, α=0, 1, …,18 representing 19 discrete speed directions, where e α Is a discrete speed distributed type:
g eq (r, t) represents an equilibrium distribution function of temperature, as shown in the following formula:
the relationship between dimensionless relaxation time τ and thermal diffusivity λ is:
typically, equal (ρc) is chosen at the time of calculation p ) The value of (ρc) as air can be used in the actual simulation p ) The value serves as a reference value. For the common solid and air in the pores, in order to reflect the difference of the heat conducting property of the two, it is ensured that (tau gf -0.5)/(τ gs -0.5)＝λ f /λ s In order to ensure convergence of simulation in the lattice unit, τ ε (0.5-2.0) is generally set.
Both the grid interface and the gas-solid boundary conditions adopt an unbalanced extrapolation format:
g α (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )-g α (ne) (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )+[g α (r,t)-g α eq (r,t)]
the corresponding macroscopic temperature and heat flux density can be determined by:
after the temperature field is determined, the effective heat conductivity lambda can be obtained eff The calculation formula of (2) is as follows:
λ eff ＝qδ/ΔT
where q is the steady state heat flow through the coating with a thickness δt, Δt representing the upper and lower boundary temperature difference.
FIG. 7 is a schematic representation of a simulated coating temperature field distribution of the present invention. At the same crack/pore ratio, fig. 7 (a) shows the layered structure coating temperature field with (a 1) no or (a 2-a 5) microcracks of different sizes. FIG. 7 (b) shows the columnar structure coating temperature field with (b 1) no or (b 2-b 5) microcracks of different sizes.
FIG. 8 is a numerical simulation of effective thermal conductivity of a coating of the present invention as a function of microcrack parameters. As can be seen from the figure, the thermal conductivity gradually decreases as the crack ratio increases. Therefore, the numerical reconstruction model of the thermal barrier coating constructed by the invention can play a certain guiding role in preparing and using the thermal barrier coating, and reflect the evolution rule of the thermal insulation performance of the thermal barrier coating.
Various modifications and variations of the present invention will be apparent to those skilled in the art in light of the foregoing teachings and are intended to be included within the scope of the following claims.
Claims (3)
1. A method for numerical reconstruction and heat transfer characteristic evaluation of a microcrack-containing thermal barrier coating microstructure, the method comprising:
s1, determining simulation areas and size settings, including settings of a physical model and a simulation calculation grid; based on a Monte Carlo simulation method and a four-parameter growth method, generating random microcracks with different morphological characteristics;
s2, changing the inclination directions of different microcracks according to a certain statistical rule through a coordinate transformation method, then placing the microcracks in a simulation area, and judging whether the space occupied by the microcracks reaches the porosity ratio of the preset microcracks or not;
s3, establishing a general pore model of the thermal barrier coating based on a four-parameter growth method, wherein a solid framework in the thermal barrier coating is used as a growth phase, pores are non-growth phases, the setting of the porosity controls the pore volume fraction of the coating, and the generation probability of a nucleation center of the solid framework is set to control the number of the pores; traversing the initial randomly distributed growth nuclear nodes, randomly growing each growth nuclear node in a three-dimensional space, controlling the generation of thermal barrier coatings of different structures according to growth nuclear probability of 26 directions under three-dimensional coordinates, wherein the growth nuclear probability of the layered structure coating in the horizontal direction is far greater than that in the vertical direction, and the columnar structure coatings are opposite;
s4, overlapping the general pore structure into a simulation area containing microcracks to generate a coating pore model coupling the microcrack defects, reconstructing the real mesoscopic morphology of TBCs, and judging whether the preset volume fraction is reached;
s5, establishing a heat transfer analysis model based on a thermal lattice Boltzmann method to calculate temperature distribution and heat conductivity heat insulation performance parameters, wherein in the step S1, a Monte Carlo algorithm is utilized to generate micro-crack morphology under a certain statistical distribution rule:
s1.1 generates random numbers uniformly distributed over the [0,1] interval:
the iterative formula of the linear congruence method for generating the random number is as follows:
x n ＝(ax n-1 +c)(modM)
wherein: a is a non-negative multiplier; c is a non-negative increment; m is a modulus, (modM) represents the remainder divided by M,
and then obtaining random numbers R uniformly distributed on the intervals of [0,1 ]:
s1.2, generating random numbers of other specified statistical distribution rules by using uniform random number calculation:
random numbers obeying other distribution types can be generated by using the uniform random numbers on the [0,1] interval generated in the step (1);
the probability density function of the uniform distribution is:
the method for calculating the random variable comprises the following steps:
x f ＝(b-a)R+a
wherein: x is x f Is the random number that is calculated; r is interval [0,1]]Random numbers uniformly distributed on the base;
s1.3, changing the orientation of microcracks by coordinate translation and rotation transformation:
the base coordinate system 0 and the dynamic coordinate system I exist, the gestures of the base coordinate system 0 and the dynamic coordinate system I are the same, the origin is not coincident, and the coordinate of any particle P fixedly connected with the coordinate system I in space in the coordinate system 0 is expressed as P 0 ＝[p 0x p 0y p 0z ] T The coordinates in the coordinate system I are denoted as P 1 ＝[p 1x p 1y p 1z } T Origin O of coordinate system I 1 In the coordinate system 0, the coordinates are
There is ∈according to vector operation rules>
Considering the posture change matrix of the coordinate system I relative to the coordinate system 0, namely considering that the relative relation between the two is the combination of translational motion between origins and pure rotation around the origins, the method comprises the following steps: />
In the same way->
Where Rot represents the basic rotation, written in a matrix in three-dimensional coordinates in the form of:
the above marks are rotated by alpha, phi and theta angles around x, y and z axes respectively;
s1.4, generating microcracks, and controlling the growth probability in the length/width direction to be 100/1 by using a QGS method to ensure that the microcracks are wedge-shaped; controlling the thickness direction of a single micro-crack to only have two layers of grids, so as to ensure that the micro-crack is approximately of a lamellar structure; then randomly generating a nucleation center point (x) according to a certain statistical distribution rule by using a Monte Carlo method 0 ,y 0 ,z 0 ) Morphology parameters of inclination phi, dip angle theta, length and number, nucleation center point (x 0 ,y 0 ,z 0 ) As the growth core center of the QGS microcrack, the length of the microcrack controls the growth probability of the microcrack in different directions, the inclination phi and the inclination angle theta are used as the basis of coordinate rotation transformation, so as to generate microcracks with different shapes, sizes and directions distributed according to a certain statistical rule, wherein in the step S4, the initial growth core node and the growth core node after growth are circularly traversed, and the condition of continuous growth of independent nodes is not involved; the growth phase can avoid the growth of microcracks in the simulation area and does not coincide with the microcracks, and the sum of the porosities of the microcracks and the common porosity is equal to the preset total porosity; 26 directions are included in the three-dimensional coordinate, wherein the 26 directions comprise 6 main directions, 12 face angle directions and 8 individual diagonal directions, a growing nuclear node is taken as a growing origin, a skeleton regenerates random numbers to non-pore adjacent points in the 6 main directions, and when the generated random numbers are smaller than the growing nuclear growth probability, the non-pore adjacent points grow to be growing phase nodes; this step is repeated until the growth phase meets a preset volume fraction.
2. The method of claim 1, wherein the control equation for heat conduction in step S5 can be described as:
wherein the subscript f represents air in the pores, s represents a solid skeleton, T represents the temperature of the material, ρ, λ and c p Respectively representing density, heat conductivity coefficient and constant pressure specific heat capacity;
based on the above, a D3Q19 thermal lattice Boltzmann model is adopted, and a temperature evolution equation is as follows:
where r is a position vector, t is time, delta t Is a time step, α=0, 1, …,18 representing 19 discrete speed directions, where e α Is a discrete speed distributed type:
g eq (r, t) represents an equilibrium distribution function of temperature, as shown in the following formula:
the relationship between dimensionless relaxation time τ and thermal diffusivity λ is:
both the grid interface and the gas-solid boundary conditions adopt an unbalanced extrapolation format:
g α (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )-g α (ne) (r+e α ,t+δ t )＝g α (eq) (r+e α ,t+δ t )+[g α (r,t)-g α eq (r,t)]
the corresponding macroscopic temperature and heat flux density can be determined by:
after the temperature field is determined, the effective heat conductivity lambda can be obtained eff The calculation formula of (2) is as follows:
λ eff ＝qδ/ΔT
where q is the steady state heat flow through the coating with a thickness δt, Δt representing the upper and lower boundary temperature difference.
3. The method for numerical reconstruction and heat transfer characteristic evaluation of microcrack-containing thermal barrier coating microstructure according to claim 2, characterized in that the values of (ρc p ) The value of (ρc) of air was used in the actual simulation p ) The value is taken as a reference value; for the common solid and air in the pores, in order to reflect the difference of the heat conducting property of the two, it is ensured that (tau gf -0.5)/(τ gs -0.5)＝λ f /λ s And τ e (0.5-2.0) in lattice units to ensure convergence of the simulation.
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